Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915296218972160 |
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| author | Menale, Marco Toscani, Giuseppe |
| author_facet | Menale, Marco Toscani, Giuseppe |
| contents | We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors. The macroscopic dynamics of their mean values follow a Lotka-Volterra system of ordinary differential equations. Unlike classical models of wealth and opinion formation, which tend to converge toward a steady-state profile, the oscillatory behavior of these densities only leads to the formation of local equilibria within the Fokker-Planck system. This makes tracking the evolution of most inequality measures challenging. However, an insightful perspective on the problem is obtained by using the coefficient of variation, a simple inequality measure closely linked to the Gini index. Numerical experiments confirm that, despite the system's oscillatory nature, inequality initially tends to decrease. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations Menale, Marco Toscani, Giuseppe General Finance Mathematical Physics Physics and Society 35Q20 35Q84 91B80 We present a possible approach to measuring inequality in a system of coupled Fokker-Planck-type equations that describe the evolution of distribution densities for two populations interacting pairwise due to social and/or economic factors. The macroscopic dynamics of their mean values follow a Lotka-Volterra system of ordinary differential equations. Unlike classical models of wealth and opinion formation, which tend to converge toward a steady-state profile, the oscillatory behavior of these densities only leads to the formation of local equilibria within the Fokker-Planck system. This makes tracking the evolution of most inequality measures challenging. However, an insightful perspective on the problem is obtained by using the coefficient of variation, a simple inequality measure closely linked to the Gini index. Numerical experiments confirm that, despite the system's oscillatory nature, inequality initially tends to decrease. |
| title | Measuring inequality in society-oriented Lotka--Volterra-type kinetic equations |
| topic | General Finance Mathematical Physics Physics and Society 35Q20 35Q84 91B80 |
| url | https://arxiv.org/abs/2505.15526 |